Simplified Random-Walk-Model-Based Kalman Filter for Slow to Moderate Fading Channel Estimation in OFDM Systems

This study deals with multi-path channel estimation for orthogonal frequency division multiplexing systems under slow to moderate fading conditions. Advanced algorithms exploit the channel time-domain correlation by using Kalman filters (KFs) based on an approximation of the time-varying channel. Recently, it was shown that under slow to moderate fading, near-optimal channel multi-path complex amplitude estimation can be obtained by using the integrated random walk (RW) model as the channel approximation. To reduce the complexity of the high-dimensional RW-KF for joint estimation of the multi-path complex amplitudes, we propose using a lower dimensional RW-KF that estimates the complex amplitude of each path separately. We demonstrate that this amounts to a simplification of the joint multi-path Kalman gain formulation through the Woodbury's identities. Hence, this new algorithm consists of a superposition of independent single-path single-carrier KFs, which were optimized in our previous studies. This observation allows us to adapt the optimization to the actual multi-path multi-carrier scenario, to provide analytic formulas for the mean-square error performance and the optimal tuning of the proposed estimator directly as a function of the physical parameters of the channel (Doppler frequency, signal-to-noise-ratio, power delay profile). These analytic formulae are given for the first-, second-, and third-order RW models used in the KF. The proposed per-path KF is shown to be as efficient as the exact KF (i.e., the joint multi-path KF), and outperforms the autoregressive-model-based KFs proposed in the literature.